2. Simple Exchange in a World of Equals
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| In this chapter we shall examine the demand and the supply of public
goods in the simplest of models, one in which there are only two persons and two goods,
one public and one private. To make simplicity absolute, we assume initially that the two
persons are identical, both as to productive capacity and as to tastes. For convenience,
we shall name these two persons Tizio and Caio, adding a touch of Italian flavor to the
analysis. We may think of these two persons as being the only inhabitants of an island in
the tropics. This allows us to use coconuts as the purely private good. Coconuts are
available to each person upon a specific outlay of time spent in gathering them, and this
outlay per coconut gathered remains constant over relevant quantities. Mosquito repelling
is the other good (service), and this is purely public or purely collective. That is to
say, the death of one mosquito benefits each man simultaneously, and is thus equally
available to each man. The service of mosquito repelling is also continuously variable,
and specific quantities can be secured by certain outlays of time on the part of either
person. The cost per unit of output remains constant over relevant quantities. |
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| Our purpose is to examine the process through which equilibrium in the
demand and the supply of both the private and the public good is attained, and to define
the characteristics of this outcome which will tend to emerge from the simplified
two-person exchange process. |
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| Examine first the situation in which the two persons act independently,
which would be the case if neither Tizio nor Caio recognizes that mosquito repelling
activity exhibits publicness. Each would then consider this activity, along with that of
gathering coconuts, as purely private, and under the conditions we have assumed (equal
tastes, equal productive capacities, constant returns) there would be no incentive to
engage in trade. Each man would proceed to reach a wholly private position of equilibrium
without trading with the other. The preliminary position sought for by each person would
be equivalent to that which would be attained in the one-person world. |
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| Figure 2.1 |
Each man's preferences for the two goods can be depicted on an orthodox indifference
map which is derived from a standard utility function. This construction for one man is
shown in Figure 2.1, on which units of the public good are measured along the vertical
axis and units of the private good along the horizontal axis. The opportunities open to
the individual are limited by his capacity to locate coconuts on the one hand and his
capacity to repel mosquitoes on the other. These opportunities are summarized in the
transformation function, which by our simplified assumptions is linear, drawn in Figure
2.1 as PP. The individual will initially seek to attain position E. He will
fail to reach this point, however, because in his calculus he does not, by our assumption,
take into account the publicness of the one good. Because of this publicness, the
activities of the two persons will necessarily be interdependent. |
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| In attempting to attain position E, the person will actually reach
F because his fellow will be making an outlay on mosquito repelling precisely
equivalent to his own. Since, by definition, the public good or service is equally
available to both persons, no matter by whom produced, the individual will find himself
with a bundle that contains double the amount of the public good that he anticipated in
making his initial decision to commit resources. |
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| F is not a position of final equilibrium, however, except under
the highly restrictive condition where the income elasticity of demand for the private
good is zero. Finding himself at F, the individual will consider it advantageous to
change his plans. He will treat the newly found public good as a simple increase in his
opportunities, in his real income, although the rate at which he can change one good into
the other will not be modified. In making new plans, the individual will try to adjust to
his apparent transformation curve P'P. |
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| Normally, he will reduce somewhat his production of mosquito repelling
and expand his production of the private good, coconuts. In the extreme case where the
income elasticity of the public good is zero, he would seek to attain an adjusted position
at G. If both goods exhibit positive income elasticity, the second sought-for
position will fall somewhere between F and G. For simplicity, assume that
the income elasticity of the public good (and, in the two-good model, for the private good
also) is unitary. In this case, the second-round objective under wholly independent
adjustment would be shown by H. |
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| This position will not be attained and for the same reason that E
was not attained; the activities of the two persons are interdependent. Adjustments will
continue to take place until a position at E* is reached, which will represent one
of final equilibrium under wholly independent behavior. Note that, geometrically, E*
is located where BC is equal to CE*. By our assumption of unitary income
elasticity the position of equilibrium is located along the ray EE*H. |
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| In describing the adjustment toward this final equilibrium we have
assumed that the publicness of the one good remains wholly hidden from the individuals in
the model. This insures that there is no strategic behavior in the adjustment process.
Tizio does not recognize that Caio's efforts provide him with benefits; therefore, he has
no incentive to modify his own behavior in the hope of securing more of the external
economies. |
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| Under the conditions assumed and with the utility function as depicted in
Figure 2.1, the introduction of strategic behavior on the part of one or both of the
persons will not modify the location of the final equilibrium position. This is insured by
the fact that the position of equilibrium, E*, lies on a higher utility level than G,
the extreme position that might be sought, and potentially attained, by one of the two
individuals who behaves strategically. As the construction makes clear, however, this
ordinal relationship between E* and G need not be present, even in the
two-person model. If this relationship is reversed, and if one of the persons succeeds in
reaching G while the other remains in E, a nonsymmetrical equilibrium of
sorts is achieved. Although the active strategist will not be in full marginal adjustment,
he will recognize that some concealing of his true preferences remains optimal. |
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| The construction of Figure 2.1 can be used to demonstrate that the
independent-adjustment equilibrium is nonoptimal in the Pareto sense. Both persons adjust
to the apparent production-possibility curve through E* parallel to PP.
Under genuine joint or cooperative behavior, the actual production-possibility curve faced
by each person is shown by PP**. Although the individual cannot act independently
on the basis of this production-possibility set, simultaneous action on the part of both
persons will allow each to move along PP**, finally attaining the optimal position,
E**. The next section discusses the attainment of this full equilibrium under
exchange agreements. |
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| The characteristics of any equilibrium depend upon the institutions under
which the private behavior of individuals takes place. In the initial model, all behavior
was assumed to be independent; no exchange or trade, no mutual agreement, no negotiation
or bargaining, were allowed. If these restrictions are dropped and the rules or
institutions changed so as to allow personal interaction, the position attained under
wholly independent adjustments will not remain one of equilibrium. |
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| Each man will now recognize that mosquito repelling is a genuinely
collective activity, and that there exist unexploited mutual gains from some trading
arrangements that insure a larger total outlay on the provision of this service. Simple
two-person, two-commodity trade is impossible, however, since both men enjoy identical
quantities of the public good. What can be traded or exchanged here is some agreement
on the part of each man to contribute working time (labor) toward the production of the
collective good, in this example, mosquito control. Tizio can "buy" Caio's
agreement to kill mosquitos (1) by agreeing to kill mosquitos himself, and/or (2) by
transferring to Caio a quantity of coconuts, the purely private good. The two alternatives
will be wholly indifferent to both men under the simplified conditions postulated. If the
two men should differ in productive capacity, however, or if there should be returns to
scale in the production of either good, comparative advantage in the ordinary sense would
determine the efficient trading arrangements. Should Tizio be relatively more efficient in
locating coconuts, he would spend all of his time in this way, and then he would
"purchase" the public good solely through maintaining Caio's private-goods
consumption. Should Caio, by contrast, be relatively more efficient in coconut gathering,
he would provide some private-goods subsistence for Tizio, while the latter carries out
the public activity of killing mosquitoes. |
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| Figure 2.2 |
The process through which trading equilibrium comes to be established may be shown in
Figure 2.2, which is an Edgeworth-box diagram converted for current purposes. Here we
measure Tizio's labor time spent in gathering coconuts for his own consumption on
the horizontal axis, and Caio's time spent in gathering coconuts for his own consumption
on the vertical axis. We assume that each man has available a fixed quantity of labor time
to devote to the production of goods, public or private, and that this time is identical
for each man. In effect, we assume that leisure is not a variable in the model. In the
orthodox sense, the origin for Tizio is at 0 , that for Caio at 0' . |
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| We now define point A as that position attained under the wholly
independent adjustment process previously discussed. Hence, 0A is the amount of
time that Tizio spends in gathering coconuts in the private-adjustment equilibrium;
similarly, 0'A is the time Caio spends on the same activity. Confronted with the
private production-possibility curves indicated by P, both persons are in
equilibrium at A. |
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| With this construction it becomes possible to generate an indifference
map for each man that will indicate his tastes for the public good and the private good,
but in such a way that exchange can be analyzed. The individual's evaluation of the public
good can be considered as an indirect evaluation of his fellow's labor time spent in
producing the good. Any upward vertical movement in Figure 2.2 represents, for Tizio, an
increase in the quantity of the public good supplied because, as Caio gives up gathering
coconuts for his own use, he must either (1) devote his time to mosquito control, or (2)
gather coconuts for Tizio's use. Similarly, any leftward horizontal movement on Figure 2.2
represents, for Caio, an increase in the quantity of the public good that is supplied to
him (as well as to Tizio). Mutually beneficial exchange can obviously take place so long
as the movement from A is in the general northwesterly direction. The position of
trading equilibrium will be located at some point along the contract locus, JK, in
Figure 2.2. At this final equilibrium, both Tizio and Caio will be giving up a specific
amount of their own time to the production, directly or indirectly, of the public good.
And more of the public good and less of the private good will be supplied than at A.
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| Bargaining strength and luck may, of course, determine the shares of the
two men in public-goods production, within limits. Since mutual gains are secured in the
shift from the no-trade position at A to a position on the contract locus, there
exist many possible distributions of these gains over inframarginal ranges. This may,
because of income effects, generate slight differences in the quantity of the public good,
but these can be neglected here. |
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| We may now examine carefully the characteristics of the position of full
trading equilibrium; that is, any point on the contract locus, JK in Figure 2.2,
where trade has stopped and all further prospects for mutual gains are eliminated. By the
standard geometry, we know that the indifference curves of the two traders are tangent; in
this respect the position is similar to that reached when trade takes place in purely
private goods. This tangency condition indicates that the marginal rates of substitution
between the two items traded are equal for the two persons. Let us define these marginal
rates of substitution precisely. |
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| Tizio is giving up units of private good, coconuts, in exchange for units
of public good, mosquito repellent, as the latter is reflected in Caio's willingness to
"supply" the second good, either through his own labor or through providing
Tizio with subsistence. Caio is in a similar position on the other side of the exchange.
There seems to be something wrong here, however, since both men value the public
good, and both must adjust to the same quantity, by definition. Something
different from simple two-person, two-commodity trade must be taking place. The mystery
here, if indeed there is one, is resolved when we recognize that all exchange is
two-sided. If there is a demander there must also be a supplier. Hence, one or both of the
two traders in our model must be supplying the public good or service to the other who is
demanding it. Let us continue, for now, to assume that there is no comparative advantage,
that each man produces an equal share of the public good that is jointly consumed by both.
Each man, therefore, is "supplying" units of the public good to the other, in
exchange for a similar supply on the part of his trading partner. Equilibrium is defined
by the standard equivalence between marginal rates of substitution. But what this
definition masks, in its simple form, is the evaluation that each man himself places on
the public good that he himself supplies to the other. In this setting, Tizio is supplying
Caio with units of public good, but in the process, he is also supplying himself. His
marginal rate of substitution is a summation of two separate components. He must consider
his own marginal evaluation of the public good, purely as a consumption item, plus his
negative marginal evaluation of the same good as this arises from his share of the supply
or production cost. |
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| This somewhat particularized interpretation of trading equilibrium is
made necessary by the publicness of one of the traded goods. The analysis may be clarified
if we assume that one of the two traders does possess a comparative advantage over the
other in producing the public good. Let us suppose that Caio can produce mosquito
repellent at a relative advantage over Tizio. The trading process will then lead to Caio
supplying all of the public good and receiving from Tizio a certain quantity of the
private good in order to maintain his own consumption of the latter. In full trading
equilibrium, Tizio's standard marginal rate of substitution in consumption between the two
goods will be equated to Caio's marginal rate of substitution in exchange. The
latter will include two components, Caio's own marginal rate of substitution in
consumption between the private and the public good, and his own marginal rate of
substitution between the two in production. This point will be further clarified in the
simple algebraic treatment of the model in the next section. |
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Algebraic Statement of Trading Equilibrium
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| The simple Tizio-Caio model of two-person, two-good trade when one of the
two goods is purely public can now be discussed with elementary algebraic tools. Any
complexities that arise in this section will be clarified in subsequent discussion.
Essentially the same formal analysis introduced here is again presented for the more
general case at the end of Chapter 4. |
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Tizio's utility function is defined as,
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(1) |
where X1 is the private good (coconuts) and X2 is
the public good (mosquito repellent). Superscripts designate the person who produces the
goods in question, directly or indirectly. Caio's utility function is defined in the same
way as,
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(2) |
For simplicity, we continue to assume that each man devotes a fixed amount of labor
input to total goods production, public and private. |
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Each man will confront a transformation function indicating the rate at
which the private good can be converted into the public good, and vice versa,
through his own behavior. These transformation functions are,
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(3)
(4) |
If each man acts independently, and no trade takes place, equilibrium will finally come
to be attained when the conditions indicated in (5) and (6) below are met. In writing
these conditions, we adopt the convention of using lower-case u's and f 's
to indicate the partial derivatives of the utility and transformation functions
respectively, with goods noted in the subscripts and persons in the superscripts. Thus,
is written as
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(5)
(6) |
These conditions are the standard ones for individual marginal adjustment; each person
modifies his own behavior so long as the marginal rate of substitution in consumption
differs from his marginal rate of transformation. |
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| We now want to see why trade takes place, how it takes place, and what
equilibrium will tend to emerge. |
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We know from the definition of a public good that a unit of x2
produced and consumed by Tizio is valued by Caio to the same extent that he values a unit
of his own production. Similarly, for Tizio's evaluation of a unit produced and consumed
by Caio. This guarantees that, in the no-trade equilibrium, Tizio's activity in producing
the public good exerts a Pareto-relevant external economy on Caio, whereas Caio's activity
in producing the public good exerts a similar externality on Tizio. Each person values the
producing activity of the other at some value greater than zero in the no-trade
equilibrium. No value will be placed by either man on the production of private goods by
the other. In algebraic language, these conditions may be stated,
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(7)
(8) |
Each person places a positive value on the marginal extension of public-goods
production by the other. Each will, therefore, be willing to "pay for" this
extension, and, in response, each will stand willing to extend his own production for any
receipt above zero. Trade will, of course, take place under such conditions, and will
continue until (9) and (10) below are satisfied.
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(9)
(10) |
As stated in (9) and (10), the conditions are fully general for two-person, two-good
exchange, and these same statements encompass any degree of externality or
"publicness" in x2. For example, suppose that x2
has been erroneously labeled as being purely public when, in fact, both Tizio and Caio
consider it to be purely private. In this case, the left-hand terms in (9) and (10) become
zero; the no-trade position is restored. Trade will not emerge under the restricted
conditions of this example where the two persons are identical with respect to tastes and
productive capacities and where production functions are constrained. As a second example,
suppose that x2 is only partially public; that is to say, Tizio values
his own mosquito repelling activity more than he does the similar activity of Caio,
although he places some positive valuation on the latter. Conditions (9) and (10) are not
modified; they remain those that must be met in full trading equilibrium. Or, to take a
less familiar variation, suppose that both x1 and x2
are purely collective. Conditions (9) and (10) continue to define equilibrium in the
two-person, two-good case. However, as we shall introduce at a later point, the
generalization here to three or more persons becomes different from that in models where
at least one purely private good exists. |
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If we postulate at the outset that one of the two goods is purely public,
as we have done in this chapter, it becomes possible to simplify greatly the statement of
the necessary conditions for equilibrium. This simplification has been implicit in most of
the statements made by those scholars who have been instrumental in developing the modern
theory of public goods. When x2 is known to be purely public, these
necessary conditions can be reduced to (9) alone if the assumption is made that only one
of the two persons produces the public good. Suppose that Caio actually produces this
good, and that Tizio pays him for the appropriately determined share through a transfer of
private goods. This allows us to transpose and to drop the now unnecessary sub- and
superscripts to get,
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(9A) |
which can be readily recognized as the familiar definition of the conditions for
public-goods optimality, as presented by Paul A. Samuelson and others. The summed marginal
rates of substitution between the public good and the private good must be equal to the
marginal rate of transformation, or, somewhat loosely, marginal cost. |
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| Note that, as these have been discussed here, the conditions (9), (9A)
and (10) have not been explicitly connected with "optimality" or
"efficiency." These conditions are presented as those which allow us to define
the characteristics of an equilibrium position, one that will tend to emerge from a
two-person trading process. Until and unless these are satisfied, mutual gains from
further trade can be shown to exist. In such situations trade will take place, provided
that we ignore, as we shall throughout most of the elementary analysis, the costs of
negotiating market agreements themselves. |
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Some Marshallian Geometry
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| One of Professor Frank Knight's favorite quotations is from Herbert
Spencer's Preface to the Data of Ethics: "Only by varied iteration can alien
conceptions be forced on reluctant minds." Since the analysis attempted here
qualifies as alien, at least to some degree and to some students, I shall heed Spencer's
advice, even at the expense of redundancy. Having presented the theory of simple exchange
in one of the most sophisticated of the economist's several languages, I shall now discuss
the same material with more mundane tools. Some rigor is necessarily lost in the process,
and the logic becomes imperfect in its details. Elementally, however, the principles that
emerge are not modified, and considerable gain may be registered toward genuinely
intuitive understanding of the exchange process. |
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| Figure 2.3 |
The tools that are most familiar to traditional micro-economists are the geometrical
constructions of Marshallian demand and supply, and these can be employed here in
analyzing trade or exchange in the mixed world that contains both private and public
goods. For expositional simplicity, it is necessary to neglect income-effect feedbacks on
individual marginal evaluations of the public good. We assume continuous variation in the
quantities of the two goods. Under these conditions, it becomes possible to derive a
single marginal evaluation schedule or curve for the public good, measured in units of the
private good, a schedule or curve that will not shift as a result of changes in the
distributions of the net gains-from-trade in the public good. Such a curve is plotted as E
in Figure 2.3. Because of our assumption that Tizio and Caio are identical with respect to
both tastes and productive capacities, the construction is simplified greatly. This allows
us to utilize the same marginal evaluation curve for each person. We can also draw in a
curve that measures the marginal cost of producing the public good. For simplicity, we
assume this to be uniform over varying quantities; this is drawn as MC in Figure
2.3. |
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| In complete independence of the other person's activity, Tizio and Caio
would each aim initially at reaching the position shown at A. In trying to do so,
however, each would find himself at A'', where double the amount of public good
anticipated is available for his own consumption. At this juncture each person will have a
strong incentive to cut back on his own production of the public good. This is because, at
the consumption margin, the marginal evaluation placed on the good falls below the
marginal cost of producing it. If action takes place instantaneously, costlessly and
simultaneously, we could expect both persons to cease production, each expecting the other
to provide the public good in the desired quantity. Under these extreme conditions, we
should expect a cyclical pattern of behavior, between no production of the public good and
an excessive amount. It seems reasonable here to make the model somewhat less restrictive
by assuming that there will be some departure, however slight, from absolute simultaneity
in adjustment. |
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| Let us suppose that Tizio, having tried to attain position A,
finds himself in position A'' slightly before Caio realizes that he too is in a
similar position. This differential in response time allows Tizio to adjust to the
external economy that Caio exerts upon him before the latter reciprocally reacts. Tizio
will immediately reduce his own production of the public good. In the case where income
effects are neglected altogether, he will reduce his own production completely, to zero.
Once he has done so, Caio has no incentive to reduce his own production below 0X1,
assuming away strategic considerations. Each person would then find himself in
private-adjustment equilibrium. Caio, who has initially tried to reach position A,
finds himself where he expected to be. He still secures some "consumer's
surplus" despite the fact that he is the only producer. Tizio, having adjusted most
quickly, enjoys the full benefits of the public-goods quantity 0X1
without cost. He secures a larger consumer's surplus than Caio. However, Tizio has no
incentive to expand his own output above zero.*5
Caio has no incentive to reduce his below 0X1. If trade is prevented,
and if strategic behavior is absent, equilibrium is attained. |
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| Strategic behavior may, of course, arise to disturb this equilibrium,
even if trade is prevented. If each person recognizes the interdependence that the
publicness of the one good necessarily introduces, he will be led, especially in a
two-person or small-number setting, to behave strategically. Each man may find it sensible
to hold off production, even below the levels that seem privately rational, in
anticipation of tricking the other partner into taking on the lion's share of the costs,
as Caio has done in our illustration. This whole matter of strategic behavior, which is
closely related to what has been called the "free-rider problem," is very
important in the theory of public goods. We shall devote considerable space to a
discussion of this problem at a later point in this book. At this early stage, it seems
best to leave the matter out of account, since it does not modify the characteristics of
equilibrium that is attained after trade takes place, and it is these characteristics, and
not the means of getting to equilibrium, that are the primary subject of attention here. |
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| We now want to demonstrate why and how trade will take place, starting
from the position of independent adjustment equilibrium. Tizio and Caio are both in
private equilibrium, with Caio producing an amount, 0X1 , of the public
good; Tizio produces nothing; both persons consume the full amount produced by Caio.
Figure 2.3 allows trade to be depicted readily. |
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| Caio finds himself at position A; Tizio finds himself in the same
position, but without having undergone any cost. The potentialities for mutually
advantageous trades become apparent when we ask the question: How much will Tizio be
willing to pay Caio for the latter's agreement to produce additional units of the public
good? And, on the other side, how much will Caio have to receive in order that he express
some willingness to produce additional units? If the first answer involves a number no
smaller than the second, trade will tend to arise. The roles of the two persons in the
questions could be reversed, of course, with Tizio rather than Caio taking on the marginal
or incremental production. |
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| Note that, beyond A, Caio still places a positive marginal
evaluation on the good, as shown by the curve, E, to the right of A. He need
only receive, as a minimum, the difference between this marginal evaluation and the
marginal cost of producing. In this way, it becomes possible to construct a supply
curve for incremental production beyond the amount 0X1. This is
derived geometrically by subtracting vertically the evaluation curve, E, from the
marginal cost curve, MC. This supply curve is labeled S in Figure 2.3. |
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| How much will Tizio be willing to pay Caio for the latter's offer to
undertake additional public-goods production? This is shown by Tizio's own marginal
evaluation of the quantities beyond the amount 0X1. Trading equilibrium
is attained when demand equals supply, or at position B, where the output 0X
is produced, in this illustration wholly by Caio, and is consumed by both persons. At this
trading equilibrium, the amount that Tizio is willing to pay Caio for the marginal
extension of production is just equal to the minimal amount that Caio is willing to
accept. There remain no unexploited gains-from-trade at the margin of adjustment. By our
neglect of income effects, the distribution of the inframarginal gains-from-trade does not
modify the position of trading equilibrium. Over the range of production between 0X1
and 0X, such gains may be shared in any one of many ways, depending on the relative
bargaining strengths and skills of the two traders. |
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| In this illustration, we have assumed that Tizio is the initial free
rider and that trade involves his payment to Caio for additional production. This
assumption does not modify the analysis. In the movement from no production to the final
position of trading equilibrium, significant gains are realized. These may be distributed
in many ways. At every point, some bargaining range will exist, and the outcome of the
two-person bargaining negotiations will determine the subsequent path toward final
equilibrium. Because of our explicit neglect of income-effect feedbacks on individual
marginal evaluations, the same quantity of public good will be produced in full trading
equilibrium regardless of the route taken to attain this equilibrium. If we drop this
simplifying assumption, the geometry becomes messy and difficult to handle, but the
characteristics of the final trading solution remain essentially the same. In this case,
however, the equilibrium quantity of the public good may be modified somewhat by the route
through which this equilibrium is attained. |
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The characteristics of the final equilibrium position are those defined
in the conditions (9) and (10) of the preceding section. In full trading equilibrium, the
marginal rate of substitution between the public good and the private good in consumption,
indicated by the marginal evaluation curve, minus marginal cost to the individual, either
incurred through producing the good himself or through paying or receiving subsidies from
his trading partner, must be zero for each person. Referring again to conditions (9) and
(10), these may be rewritten in the measurements of Figure 2.3 as follows:
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(9-2.3)
(10-2.3) |
In the more familiar language of the modern theory of public goods, which implicitly
assumes that only one person produces all of the public good, we can say that the summed
marginal rates of substitution equal the marginal cost of, in terms of Figure 2.3,
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(9A-2.3) |
which is, of course, the same condition restated. |
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| The theory of private-goods exchange is rigorously developed in Peter
Newman's book [The Theory of Exchange (Englewood Cliffs, N.J.: Prentice-Hall,
1965)]. Although his analysis is presented axiomatically, his procedure in moving from the
simple to the more complex trading models closely parallels that which is followed in this
book. |
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| To my knowledge, the theory of public goods has not been presented in
terms of the simple models of two-person exchange developed in this chapter, although the
"voluntary exchange theory," especially in the Erik Lindahl formulation, can be
interpreted in this way [Die Gerechtigkeit der Besteuerung (Lund, 1919), translated
as "Just Taxation—A Positive Solution," and included in Classics in the
Theory of Public Finance, edited by R. A. Musgrave and A. T. Peacock (London:
Macmillan, 1958), pp. 168-76]. The basic Lindahl model has been interpreted in modern
terms by Leif Johansen ["Some Notes on the Lindahl Theory of Determination of Public
Expenditures," International Economic Review, IV (September 1963), 346-58]. |
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| The independent-adjustment outcome in the presence of public-goods
phenomena has been discussed by James M. Buchanan and Milton Z. Kafoglis and by Buchanan
and Gordon Tullock [Buchanan and Kafoglis, "A Note on Public Goods Supply," American
Economic Review, LIII (June 1963), 403-14; Buchanan and Tullock, "Public and
Private Interaction Under Reciprocal Externality," in The Public Economy of Urban
Communities, edited by J. Margolis (Resources for the Future, 1965), pp. 52-73]. |
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| Although they are not directly relevant to the elementary discussion of
this chapter, the basic contributions to the modern theory of public goods first of all by
Knut Wicksell and then by Paul A. Samuelson and R. A. Musgrave should be cited early,
along with the valuable survey papers by J. G. Head [Wicksell, Finanztheoretische
Untersuchungen (Jena: Gustav Fisher, 1896), a major portion of which is translated as
"A New Principle of Just Taxation," and included in Classics in the Theory of
Public Finance, edited by R. A. Musgrave and A. T. Peacock (London: Macmillan, 1958),
pp. 72-118; Samuelson, "The Pure Theory of Public Expenditure," Review of
Economics and Statistics, XXXVI (November 1954), 387-89; "Diagrammatic Exposition
of a Theory of Public Expenditure," Review of Economics and Statistics, XXXVII
(November 1955), 350-56; Musgrave, The Theory of Public Finance (New York:
McGraw-Hill, 1959), especially Chapter 4; Head, "Public Goods and Public
Policy," Public Finance, XVII (No. 3, 1962), 197-221; "The Welfare
Foundations of Public Finance Theory," Rivista di diritto finanziario e scienza
delle finanze (May 1965)]. In his monograph, Kafoglis also provides a useful summary
of the theory [Welfare Economics and Subsidy Programs, University of Florida
Monographs in Social Science, No. 11, Summer 1961]. In his introduction to the second
edition of his book, William J. Baumol summarizes recent developments in the theory of
public goods in the context of general developments in theoretical welfare economics [Welfare
Economics and the Theory of the State, Second edition (Cambridge: Harvard University
Press, 1965), pp. 1-48]. |
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| In papers that have come to my attention only after the manuscript of
this book was substantially in its final form both Samuelson and Musgrave re-examine and
reinterpret their own earlier contributions. In the process, several ambiguities are
clarified [Samuelson, "Pure Theory of Public Expenditure and Taxation"
(Mimeographed, September 1966); Musgrave, "Provision for Social Goods"
(Mimeographed, September 1966)]. Both of these papers were prepared for the Biarritz
conference organized by the International Economic Association, and, presumably, they will
appear eventually in the published conference volume. |
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